(2x-4)(x)=50

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Solution for (2x-4)(x)=50 equation: 


Simplifying
(2x + -4)(x) = 50

Reorder the terms:
(-4 + 2x)(x) = 50

Reorder the terms for easier multiplication:
x(-4 + 2x) = 50
(-4 * x + 2x * x) = 50
(-4x + 2x2) = 50

Solving
-4x + 2x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + -4x + 2x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + -2x + x2 = 0

Solving
-25 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -2x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -2x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2x + x2 = 0 + 25
-2x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-2x + x2 = 25

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 25 + 1

Reorder the terms:
1 + -2x + x2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + -2x + x2 = 26

Factor a perfect square on the left side:
(x + -1)(x + -1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + -1) equal to 5.099019514 and -5.099019514.


Subproblem 1
x + -1 = 5.099019514

Simplifying
x + -1 = 5.099019514

Reorder the terms:
-1 + x = 5.099019514

Solving
-1 + x = 5.099019514

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 5.099019514 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.099019514 + 1
x = 5.099019514 + 1

Combine like terms: 5.099019514 + 1 = 6.099019514
x = 6.099019514

Simplifying
x = 6.099019514


Subproblem 2
x + -1 = -5.099019514

Simplifying
x + -1 = -5.099019514

Reorder the terms:
-1 + x = -5.099019514

Solving
-1 + x = -5.099019514

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = -5.099019514 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.099019514 + 1
x = -5.099019514 + 1

Combine like terms: -5.099019514 + 1 = -4.099019514
x = -4.099019514

Simplifying
x = -4.099019514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.099019514, -4.099019514}
Solution
x = {6.099019514, -4.099019514}

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